I'm interested in solo mining on Litecoin. Where can I learn about (or what math is required) two tell if this is feasible/profitable?
Currently I have 30+ CPUs running as solo miners for 40 hours and so far nothing has turned up. Are there any optimizations I should do to the miner?

I don't recommend solo mining with CPU only, it would take a really long time to find a block. If you don't like pool mining, you can download the pool software and run your own private pool where you will connect all your CPUs.

If it is profitable depends on your expenses. Generally speaking using CPU to mine BTC/LTC if you have to pay the electricity is not profitable any longer. But if you don't pay the electricity (for example is included in server hosting costs) and already have the CPUs/servers available, then your expenses are zero. So even if you would earn one cent per month it would be profitable :)